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Physical Review A

Short-pulse photoexcitation process in the hydrogen atom

A. A. Mityureva, Valery V Smirnov, A B Bichkov

Published Jan 6, 2009• 7 citations
Publisher

Abstract

A short-pulse photoexcitation of $1s\ensuremath{\rightarrow}2s,2p$ transitions in the hydrogen atom is studied with perturbation theory and the finite-element method giving an almost exact solution of the time-dependent Schrodinger equation.

DOI
10.1103/physreva.79.013402

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A short-pulse photoexcitation of 1s\ensuremath→2s,2p1s\ensuremath{\rightarrow}2s,2p1s\ensuremath→2s,2p transitions in the hydrogen atom is studied with perturbation theory and the finite-element method giving an almost exact solution of the time-dependent Schrodinger equation.
Abstract The dynamics of photoexcitation of the hydrogen atom in the discrete and continuous spectra under the action of laser pulses in the attosecond range of time and pulse durations has been analyzed using perturbation theory. It is shown that over time interval shorter than or on the order of pulse duration, the time dependence of the photoexcitation probability is generally oscillating by nature. It has been established that for certain values of parameters, the envelope of this dependence has a peak, the position of which is determined by the pulse duration and carrier frequency.
The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration as well as the dependence on the carrier phase with respect to the pulse envelope. It should be noted that if the dependence of the probability W on the phase manifests itself either only for very short pulses, when ωt 1 too for fields of moderate strength, when the perturbation theory is applicable. The present work is dedicated to the theoretical analysis of two-photon excitation of hydrogen atom in a discrete energy spectrum by ultrashort electromagnetic pulses of femto- and subfemtosecond ranges of durations. As examples, excitation of hydrogen atom from the ground state to excited states with a zero orbital moment is considered.
We have discussed the problems of non linear interaction between electromagnetic radiations with atoms from semi-classical point of view. Time dependent Schrödinger equation for single electron system is solved by using perturbative technique to obtain transition probability. Higher order perturbation is also discussed which is used in multiple processes, in which two or more quanta are emitted instead of a single photon. The theory is based on assumption that the perturbation is small. From this transition probability ionization rate and absorption cross-section of hydrogen atom is calculated. Its variation with photon energy and field strength is analyzed which agrees very well with experimental observations.The Himalayan PhysicsVol. 3, No. 32012Page : 40-43
Some phenomena cannot be solved using the exact solution of the Schrödinger equation. However, using approximated methods such as perturbation theory we are able to obtain remarkable results considering terms up to second order. The physical phenomena studied here are the absorption and stimulated emission by the classical feature. In addition, we are going to discuss the physical meaning of perturbation theory when we treat the behaviour how initial state ket evolves as time goes on. We will evaluate the transition of probability between states, the rate and the energy involved in the atomic transitions. It will be introduced fundamental concepts of quantum mechanics, such as interaction picture, and a general perturbation theory using constant and sinusoidal time-dependent perturbation term. Concerning to these phenomena, we considered the perturbed term of the Hamiltonian of the interaction between the vector potential and electron momentum.
In the previous chapters, we have shown how to solve the Schrodinger equation for several systems as a particle in an infinite and finite potential well, scattering, harmonic oscillator, and hydrogen atom. For all these systems, we were able to solve Schrodinger's equation exactly. However, there are complicated potentials for which Schrodinger's equation cannot be solved exactly. For such situations, we resort to approximation methods for finding approximate solutions to the Schrodinger equation. In this chapter, we discuss several approximate methods for solving Schrodinger's equation.